Astrophysics > Earth and Planetary Astrophysics

Title:Low-Eccentricity Migration of Ultra-Short Period Planets in Multi-Planet Systems

Abstract: Recent studies suggest that ultra-short period planets (USPs), Earth-sized
planets with sub-day periods, constitute a statistically distinct sub-sample of
{\it Kepler} planets: USPs have smaller radii ($1-1.4R_\oplus$) and larger
mutual inclinations with neighboring planets than nominal {\it Kepler} planets,
and their period distribution is steeper than longer-period planets. We study a
"low-eccentricity" migration scenario for the formation of USPs, in which a
low-mass planet with initial period of a few days maintains a small but finite
eccentricity due to secular forcings from exterior companion planets, and
experiences orbital decay due to tidal dissipation. USP formation in this
scenario requires that the initial multi-planet system have modest
eccentricities ($\gtrsim 0.1$) or angular momentum deficit. During the orbital
decay of the inner-most planet, the system can encounter several apsidal and
nodal precession resonances that significantly enhance eccentricity excitation
and increase the mutual inclination between the inner planets. We develop an
approximate method based on eccentricity and inclination eigenmodes to
efficiently evolve a large number of multi-planet systems over Gyr timescales
in the presence of rapid (as short as $\sim 100$~years) secular planet-planet
interactions and other short-range forces. Through a population synthesis
calculation, we demonstrate that the "low-$e$ migration" mechanism can
naturally produce USPs from the large population of {\it Kepler} multis under a
variety of conditions, with little fine tuning of parameters. This mechanism
favors smaller inner planets with more massive and eccentric companion planets,
and the resulting USPs have properties that are consistent with observations.